Sub Discipline: DEPARTMENTAL CORE

Page 1 of 12

SUMMARY OF COURSES

Sub Discipline: DEPARTMENTAL CORE

SUBJECT

CODE

SUBJECT L-T-P CREDIT DEVELOPER

MAC01 MATHEMATICS 1 3-1-0 4



Basket of Open Elective-1 [4th semester]

SUBJECT

CODE


MAO441 Discrete Mathematics 3-0-0 3

MAO442 Probability and Stochastic

Processes

3-0-0 3


SUBJECT

CODE


MAO541 Mathematical Methods for

Engineers

3-0-0 3

MAO542 Linear Algebra 3-0-0 3

MAO543 Modern Algebra 3-0-0 3


SUBJECT

CODE


MAO841 Operations Research 3-0-0 3

MAO842 Advanced Numerical Analysis 3-0-0 3

MAO843 Optimization Techniques 3-0-0 3

Page 2 of 12

Department of Mathematics

Course

Code

Title of the course Program Core

(PCR) /

Electives (PEL)

Total Number of contact hours Credit

Lecture

(L)

Tutorial

(T)

Practical

(P)

Total

Hours

MAC 01

MATHEMATICS - I PCR 3 1 0 4 4

Pre-requisites Basic concepts of function, limit, differentiation and integration. Course

Outcomes CO1: Fundamentals of Differential Calculus CO2: Fundamentals of Integral Calculus CO3: Fundamentals of Vector Calculus CO4: Basic Concepts of Convergence

Topics

Covered

Functions of Single Variable: Rolle’s Theorem and Lagrange’s Mean Value Theorem

(MVT), Cauchy's MVT, Taylor’s and Maclaurin’s series, Asymptotes & Curvature

(Cartesian, Polar form). (8)

Functions of several variables: Function of two variables, Limit, Continuity and

Differentiability, Partial derivatives, Partial derivatives of implicit function, Homogeneous

function, Euler’s theorem and its converse, Exact differential, Jacobian, Taylor's &

Maclaurin's series, Maxima and Minima, Necessary and sufficient condition for maxima and

minima (no proof), Stationary points, Lagrange’s method of multipliers. (10)

Sequences and Series: Sequences, Limit of a Sequence and its properties, Series of positive

terms, Necessary condition for convergence, Comparison test, D Alembert’s ratio test,

Cauchy’s root test, Alternating series, Leibnitz’s rule, Absolute and conditional

convergence. (6)

Integral Calculus: Mean value theorems of integral calculus, Improper integral and it

classifications, Beta and Gamma functions, Area and length in Cartesian and polar co-

ordinates, Volume and surface area of solids of revolution in Cartesian and polar forms, (12)

Multiple Integrals: Double integrals, Evaluation of double integrals, Evaluation of triple

integrals, Change of order of integration, Change of variables, Area and volume by double

integration, Volume as a triple integral. (10)

Vector Calculus: Vector valued functions and its differentiability, Line integral, Surface

integral, Volume integral, Gradient, Curl, Divergence, Green’s theorem in the plane

(including vector form), Stokes’ theorem, Gauss’s divergence theorem and their

applications. (10)

Text Books,

and/or

reference

material

Text Books: 1. E. Kreyszig, Advanced Engineering Mathematics: 10 th edition, Wiley India Edition. 2. Daniel A. Murray, Differential and Integral Calculus, Fb & c Limited, 2018. 3. Marsden, J. E; Tromba, A. J.; Weinstein: Basic Multivariable Calculus, Springer, 2013.

Reference Books: 1. Tom Apostal, Calculus-Vol-I & II, Wiley Student Edition, 2011. 2. Thomas and Finny: Calculus and Analytic Geometry, 11 th Edition, Addison Wesley.

Page 3 of 12


Course

Code


(PCR) / Electives

(PEL)


Lecture

(L)

Tutorial

(T)

Practical

(P)

Total

Hours

MAC 02

MATHEMATICS - II PCR 3 1 0 4 4

Pre-requisites Basic concepts of set theory, differential equations and probability. Course

Outcomes CO1: Develop the concept of basic linear algebra and matrix equations so as to apply

mathematical methods involving arithmetic, algebra, geometry to solve problems.

CO2: To acquire the basic concepts required to understand, construct, solve and interpret

differential equations.

CO3: Develop the concepts of Laplace transformation & Fourier transformation with its

property to solve ordinary differential equations with given boundary conditions which

are helpful in all engineering & research work.

CO4: To grasp the basic concepts of probability theory Topics

Covered

Elementary algebraic structures: Group, subgroup, ring, subring, integral domain, and field.

(5)

Linear Algebra: Vector space, Subspaces, Linear dependence and independence of vectors,

Linear span, Basis and dimension of a vector space. Rank of a matrix, Elementary

transformations, Matrix inversion, Solution of system of Linear equations, Eigen values and

Eigen vectors, Cayley-Hamilton Theorem, Diagonalization of matrices. (15)

Ordinary Differential Equations: Existence and uniqueness of solutions of ODE (Statement

Only), Equations of first order but higher degree, Clairaut’s equation, Second order differential

equations, Linear dependence of solutions, Wronskian determinant, Method of variation of

parameters, Solution of simultaneous equations. (12)

Fourier series: Basic properties, Dirichlet conditions, Sine series, Cosine series, Convergence.

(4)

Laplace and Fourier Transforms: Laplace transforms, Inverse Laplace transforms,

Convolution theorem, Applications to Ordinary differential equations.

Fourier transforms, Inverse Fourier transform, Fourier sine and cosine transforms and their

inversion, Properties of Fourier transforms, Convolution. (10)

Probability: Historical development of the subject and basic concepts, Axiomatic definition

of probability, Examples to calculate probability, Random numbers. Random variables and

probability distributions, Binomial distribution, Normal distribution. (10)

Text Books,

and/or

reference

material

Text Books:

1. E. Kreyszig, Advanced Engineering Mathematics: 9th edition, Wiley India Edition.

2. Gilbert Strang, Linear algebra and its applications (4th Edition), Thomson (2006).

3. Shepley L. Ross, Differential Equations, 3rd Edition, Wiley Student Edition.

Reference Books:

1. S. Kumaresan, Linear algebra - A Geometric approach, Prentice Hall of India (2000).

2. C. Grinstead, J. L. Snell, Introduction to Probability, American Mathematical Society.

Page 4 of 12


Course

Code


(PCR) /

Electives

(PEL)


Lecture

(L)

Tutorial

(T)

Practical

(P)

Total

Hours

MAC331

MATHEMATICS-III PCR 3 1 0 4 4

Pre-requisites Basic knowledge of topics included in MAC01 & MAC02

Course

Outcomes CO1: Acquire the idea about mathematical formulations of phenomena in physics and

engineering.

CO2: To understand the common numerical methods to obtain the approximate

solutions for the intractable mathematical problems.

CO3: To understand the basics of complex analysis and its role in modern mathematics

and applied contexts.

CO4: To understand the optimization methods and algorithms developed for

solving various types of optimization problems.

Topics

Covered

Partial Differential Equations (PDE): Formation of PDEs; Lagrange method for solution

of first order quasilinear PDE; Charpit method for first order nonlinear PDE; Homogenous

and Nonhomogeneous linear PDE with constant coefficients: Complimentary Function,

Particular integral; Classification of second order linear PDE and canonical forms; Initial &

Boundary Value Problems involving one dimensional wave equation, one dimensional heat

equation and two dimensional Laplace equation. [14]

Numerical Methods: Significant digits, Errors; Difference operators; Newton's Forward,

Backward and Lagrange’s interpolation formulae; Numerical solutions of nonlinear

algebraic/transcendental equations by Bisection and Newton-Raphson methods; Trapezoidal

and Simpson’s 1/3 rule for numerical integration; Euler’s method and modified Eular's

methods for solving first order differential equations. [14]

Complex Analysis: Functions of complex variable, Limit, Continuity and Derivative;

Analytic function; Harmonic function; Conformal transformation and Bilinear

transformation; Complex integration; Cauchy’s integral theorem; Cauchy’s integral formula;

Taylor’s theorem, Laurent’s theorem (Statement only); Singular points and residues;

Cauchy’s residue theorem. [17]

Optimization:

Mathematical Preliminaries: Hyperplanes and Linear Varieties; Convex Sets, Polytopes

and Polyhedra.

[2]

Linear Programming Problem (LPP): Introduction; Formulation of linear programming

problem (LPP); Graphical method for its solution; Standard form of LPP; Basic feasible

solutions; Simplex Method for solving LPP. [9]

Text Books,

and/or

reference

material

Text Books:

1. An Elementary Course in Partial Differential Equations-T. Amarnath

2. Numerical Methods for scientific & Engineering Computation- M.K.Jain,

S.R.K. Iyengar & R.K.Jain.

3. Foundations of Complex Analysis- S. Ponnuswami

4. Operations Research Principles and Practices- Ravindran, Phillips, Solberg

5. Advanced Engineering Mathematics- E. Kreyszig

Reference Books:

1. Complex Analysis-L. V. Ahfors

2. Elements of partial differential equations- I. N. Sneddon

3. Operations Research- H. A. Taha

Page 5 of 12


Course

Code


(PCR) /

Electives (PEL)


Lecture

(L)

Tutorial

(T)

Practical

(P)

Total

Hours

MAO441

Discrete

Mathematics

PEL 3 0 0 3 3

Pre-requisites Course Assessment methods (Continuous (CT), Mid-term assessment

(MA) and end assessment (EA))

Set Theory CT+EA

Course

Outcomes CO1: To enable the students to apply the basic concept of Logic to solve engineering

and Artificial Intelligence related problems.

CO2: To enable the students to solve problems of combinatorics.

CO3: Students will have knowledge of Graph Theory which arises in many engineering

and physical problems.

Topics

Covered

1. Introduction to set theory; combination of sets; power sets; finite and infinite sets,

Introduction to Combinatorics, Counting techniques, The inclusion-exclusion

principle, The pigeon-hole principle and its applications, Recurrence relation,

Generating function, Partial order relations; POSETS. [6]

2. Mathematical logic, Predicate logic, Basic logical operation, Truth tables, Logic

proposition and proof, Notion of interpretation, Method of proofs, Validity,

consistency and completeness. [6]

3. Propositional Calculus: Well-formed formulas, Tautologies, Equivalence, Normal

forms, Truth of algebraic systems, Calculus of predicates, Different forms of the

principle of mathematical induction. [5]

4. Relations, Equivalence relation and equivalence classes, Diagraphs, Computer

representation of relations, Warshall’s algorithm, Representations of relations by

binary matrices and digraphs; operations on relations. Closure of a relations;

reflexive, symmetric and transitive closures. [7]

5. Lattice Theory and Introduction to Boolean algebra and Boolean functions, Different

representations of Boolean functions, Application of Boolean functions to synthesis

of circuits, Composition of function, functions for computer Science, Permutation

function and growth of functions. [5]

6. Introduction of discrete numeric functions, Asymptotic behavior, Generating

functions, Linear recurrence relations with constant coefficients (homogeneous and

non-homogeneous cases), Solution of linear recurrence relations using generating

functions. [5]

7. Path, cycles, Handshaking theorem, Bipartite graphs, Sub-graphs, Graph

isomorphism, Operations on graphs, Eulerian graphs and Hamiltonian graphs, Planar

graphs, Euler formula, Traveling salesman problem, Shortest path algorithms,

Minimum spanning tree algorithms, Maximum flow algorithms. [7]

Text Books,

and/or

reference

material

Text Books:

1. Discrete Mathematics and its Applications - Kenneth H. Rosen 7th Edition -Tata

McGraw Hill Publishers – 2007.

2. Elements of Discrete Mathematics, C. L Liu, McGraw-Hill Inc, 1985. Applied

Combinatorics, Alan Tucker, 2007.

Reference Books:

1. Concrete Mathematics, Ronald Graham, Donald Knuth, and Oren Patashnik, 2nd

Edition - Pearson Education Publishers - 1996.

2. Combinatorics: Topics, Techniques, Algorithms by Peter J. Cameron, Cambridge

University Press, 1994 (reprinted 1996). Topics in Algebra, I.N. Herstein, Wiley,

1975.

Page 6 of 12


Course

Code


(PCR) /

Electives (PEL)


Lecture

(L)

Tutorial

(T)

Practical

(P)

Total

Hours

MAO442 Probability and

Stochastic

Processes

PEL 3 0 0 3 3

Pre-requisites Knowledge of differential and integral calculus, basics of probability at

MAC02

Course

Outcomes CO1: To provide the basics of probability theory.

CO2: Introduce to students the probability models in physics, engineering, biology etc.

CO3: To highlight the roles of stochastic processes in physics, social science, finance

etc.

Topics

Covered

Introduction: Axiomatic definition of Probability, Conditional Probability and

Multiplication Rules, Stochastic independence, Baye’s theorem and applications. (8)

Random Variables & Probability Distribution: Random variables: Discrete and

continuous, discrete and continuous probability distributions, Binomial and Poisson

distribution, Normal distribution, Exponential distribution, Joint probability distributions,

bivariate normal distribution. (6)

Mathematical Expectation: Expectation of random variable, Properties of Expectation,

Variance and covariance of random variables, Means and variances of Linear Combinations

of Random Variables, Conditional Expectations. Correlation coefficient. (6)

Functions of Random Variable: Transformation of Variables, Moments and Moment

Generating Functions, Characteristics functions. , Normal Approximation to Binomial. (6)

Stochastic Processes: Stochastic Process: definition and examples, Stationary Processes,

Auto correlation, Auto Covariance, cross correlative coefficient, Martingales. (6)

Markov Chains: Definitions and examples of Markov chains, Chapman- Kolmogorov

Equations & classification of states, Ergodic Markov Chain, Applications of Markov chains,

Time reversible Markov chains. (6)

Poisson Process: Poisson Process, Inter-arrival & waiting time distributions, Non-

homogeneous Poisson Process, Conditional Poisson process. (4)

Text Books,

and/or

reference

material

Text Books:

1. T. Veerarajan: Probability, Statistics and Random Process, Tata McGraw-Hill

Education, 2002.

2. Ronald E Walpole and Raymond H Myers: Probability and Statistics for Engineers

and Scientists

3. J. Medhi, Stochastic Process, Wiley Eastern Limited, Second Edition, 1994.

Page 7 of 12


Course

Code


(PCR) /

Electives (PEL)


Lecture

(L)

Tutorial

(T)

Practical

(P)

Total

Hours

MAO541

Mathematical

methods for

engineers

PEL 3 0 0 3 3

Pre-requisites Course Assessment methods (Continuous (CT), Mid-term assessment

(MA) and end assessment (EA))

MAC02 (Mathematics-II) CT+EA

Course

Outcomes CO1: To enable the students to apply integral transforms to problems formulated on

finite or infinite domains and also to solve engineering and physical problems involving

PDEs in a simpler way using integral transforms.

CO2: To enable the students to solve a discrete systems using Z- Transform.

CO3: Students will have an in-depth knowledge of power series solution of differential

equations and also will learn about special functions which arise in many engineering

and physical problems.

Topics

Covered

Difference Equations: Formation of difference equation, First and higher order difference

equations, Reduction of non-linear difference equation into linear form, Solution of

difference equations. (6)

Z-transform: Some standard Z- transforms, Properties of Z-transform, Damping rule,

Shifting rule, Initial and final value theorem, Convolution theorem, Inverse Z-transform,

Solution of difference equations using Z-transform. (6)

Series Solution of Ordinary Differential Equations: Validity of series solution, Series

solution about an ordinary point and about a regular singular point, Bessel's equation and

Bessel functions, Recurrence relations of Bessel functions, Generating function for Jn(x),

Orthogonality of Bessel functions, Legendre's equation and Legendre functions, Legendre

polynomial, Rodrigue's formula, Generating function for Pn(x), Recurrence relations for

Pn(x), Orthogonality of Legendre polynomial. (15)

Application of Fourier Transforms: recapitulation of Fourier transform & its properties,

solution of partial differential equations using Fourier transform (6)

Application of Fourier Transforms in mathematical statistics (2)

Finite Fourier Transforms: Finite Fourier Sine & Cosine transform, basic properties,

applications of finite Fourier Sine & Cosine transform in the solution of boundary value

problems (7)

Text Books,

and/or

reference

material

Text Books:

1. S. L. Ross: Differential Equations: John Willey and Sons.

2. I. N. Sneddon: The use of Integral Transforms, McGraw-Hill, 1974.

3. E. Kreyszig: Advanced Engineering Mathematics: 9thedition, Wiley India Edition.

Reference Books:

1. M.D. Raisinghania: Advanced differential equations: S.Chand Publication.

2. L. Debnath & D. Bhatta: Integral Transforms and their applications: 2nd Edition, Chapman

& Hall/CRC.

Page 8 of 12

Department of mathematics

Course

Code


(PCR) /

Electives (PEL)


Lecture

(L)

Tutorial

(T)

Practical

(P)

Total

Hours

MAO542

Linear Algebra PEL 3 0 0 3 3

Pre-requisites MAC02

Course Assessment methods

(Continuous (CT) and end

assessment (EA))

CT+EA

Course

Outcomes CO1: Solve systems of linear equations using several methods, including Gaussian

elimination and matrix inversion

CO2: Demonstrate understanding of the concepts of vector space and subspace, linear

independence, span, and basis and use these for analysis of matrices and systems of linear

equations.

CO3: Determine eigenvalues and eigenvectors and solve eigenvalue problems; apply

principles of matrix algebra to linear transformations; discriminate between

diagonalizable and non-diagonalizable matrices; demonstrate understanding of inner

products and associated norms.

Topics

Covered Systems of linear equations, Matrices, Elementary row and column operations, Row-

reduced echelon matrices., Gaussian elimination, LU-Decomposition. (6)

Vector spaces, Subspaces, Linear span, Linear dependence and independence, Basis and

dimension, Ordered basis and coordinates, Row space and column space, Direct-sum

decompositions. (12)

Linear transformations, Rank-Nullity theorem, Matrix representation of linear

transformations. (7)

Eigenvalues and eigenvectors, Cayley-Hamilton theorem, Diagonalization of Matrices,

Minimal polynomial, Rational canonical form, Jordan canonical form. (13)

Inner Product Spaces, Orthonormal Basis, Gram-Schmidt Theorem. (4)

Text Books,

and/or

reference

material

Text Books:

1. K. Hoffman and R. Kunze, Linear Algebra, Prentice Hall of India, New Delhi, 1990.

2. S. K. Mapa, Higher Algebra, Sarat Book Distribution, 2000.

Reference Books:

1. S. Lang, Linear Algebra, Springer, Third Edition.

2. S. Kumaresan, Linear Algebra: A Geometric Approach, PHI Learning Pvt. Ltd., 2000.

Page 9 of 12

Department of Mathematics Course

Code


(PCR) /

Electives (PEL)


Lecture

(L)

Tutorial

(T)

Practical

(P)

Total

Hours

MAO543

Modern Algebra PEL 3 0 0 3 3

Pre-requisites Course Assessment methods (Continuous (CT) and end assessment

(EA)) NIL CT+EA

Course

Outcomes CO1: Acquire an idea about abstract mathematical problems CO2: To understand the principle of symmetric objects CO3: To learn the basic tools of vector spaces, coding theory and cryptography

Topics

Covered

Preliminary concept: Sets and Equivalence relations and partitions, Division algorithm for

integers, primes, unique factorizations, Chinese Remainder Theorem, Euler ф-function. [10]

Groups: Cyclic groups, Permutation groups, Isomorphism of groups, Cosets and Lagrange's

Theorem, Normal subgroups, Quotient groups, Group homomorphisms, Cayley’s theorem,

Cauchy’s theorem. [12]

Rings: Ideals and Homomorphism, Prime and Maximal Ideals, Quotient Field of an Integral

Domain, Polynomial Rings. [10]

Fields: Vector space, Field extensions, Finite Fields. [10]

Text Books,

and/or

reference

material

Text Books:

1. J. B. Fraleigh, A First Course in Abstract Algebra, Addison Wesley, 2013.

2. I. N. Herstein, Topics in Abstract Algebra, Wiley Eastern Limited, 1975.

Reference Books:

1. T. W. Hungerford, Algebra, Springer, 2009.

2. D. S. Dummit, R. M. Foote, Abstract Algebra, Second Edition, John Wiley & Sons,

Inc., 1999.

3. G. A. Gallian, Contemporary Abstract Algebra, Narosa Publishers, 2017.

Page 10 of 12


Course

Code


(PCR) /

Electives (PEL)


Lecture

(L)

Tutorial

(T)

Practical

(P)

Total

Hours

MAO841

Operations Research PEL 3 0 0 3 3

Pre-requisites Basic concepts of Set Theory, Linear Programming Problem, Network and

Game Theory Course

Outcomes CO1: Origin of Operations Research and Formulation of Problem. CO2: Fundamentals of Linear Programming and its applications. CO3: Fundamentals of Network Analysis. CO4: Basic Concepts of Game Theory.

Topics

Covered

Overview of Operations Research: Origin of OR and its definitions, Formulation of the OR

problems, Developing OR models, Testing the adequacy of the model, Model solution,

Evaluation of the solution and implementation. (4)

Linear Programming and its Applications: Vector spaces, Basis, Linear transformations,

Convex sets, Extreme points and convex polyhedral sets Theory of Simplex method, Simplex

Algorithm, Degeneracy, Duality theory, primal dual algorithms, Transportation problems,

Assignment problems, Sensitivity analysis. (14)

Network Analysis: Introduction to network analysis, Shortest path problem, Construction of

minimal spanning tree, Flows in networks, Maximal flow problems. Definition of a project,

Job and events, Construction of arrow diagrams, Determination of critical paths and calculation

of floats. Resource allocation and least cost planning, Use of network flows for least cost

planning. Uncertain duration and PERT, PERT COST system. Crashing. (12)

Game Theory: Maxmin and Minmax principle, Two-person Zero-sum games with saddle

point, Game problems without saddle point, Pure strategy and mixed strategy, Solution of a

2×2 game problem without saddle point, Graphical method of solution for n×2 and 2×n game

problem, Reduction rule of a game problem (Dominance rule), Algebraic method of solution

of game problem without saddle point, Reduction of a game problem to linear programming

problem. (12) Text Books,

and/or

reference

material

Text Books: 1. J. K. Sharma: Fundamentals of Operations Research, Macmillan. 2. F.S. Hiller and G. J. Leiberman, Introduction to Operations Research (6th Edition),

McGraw-Hill International Edition, 1995. 3. Ravindran, Philips, Solberg, Operations Research Principles and Practices, Wiley India

Edition.

Reference Books: 1. Kanti Swarup, P. K. Gupta and Man Mohan, Operations Research- An Introduction, S.

Chand & Company.

2. Anderson, D. R., Sweeney, D. J. and Williams, T. A., An Introduction to

Management Science, St. Paul West Publishing Company, 1982.

3. Sharma, S. D., Operations Research, Kedar Nath and Ram Nath, Meerut, 1995.

4. H. A. Taha, Operations Research –An introduction, PHI

Page 11 of 12


Course

Code


(PCR) /

Electives (PEL)

Total contact hours (Per week) Credit

Lecture

(L)

Tutorial

(T)

Practical

(P)

Total

Hours

MAO842

Advanced

Numerical Analysis

PEL 3 0 0 3 3

Pre-requisites Course Assessment methods (Continuous (CT) and end assessment

(EA))

Basics of Linear Algebra &

Numerical Methods

CT+EA

Course

Outcomes CO1: Develop problem solving skills by different numerical methods and also skill in

numerically verifying theoretical convergence speed.

CO2: Help to work with key concepts of stability and assessing the accuracy of

numerical results.

CO3: Help to write algorithm, computational steps & flow chart which help in

developing computer program.

CO4: Help to solve various scientific and engineering problems by different numerical

methods.

Topics

Covered

(with lecture

hours)

Numerical solution of Algebraic and transcendental equations (Method of Iteration,

Newton-Raphson method), convergence and errors. (3)

Solution of system of equations by Direct method (Gauss-elimination, Gauss Jordon, L-U

decomposition) and Iteration method (Jacobi, Gauss-Seidel), Convergence analysis and

errors. (7)

Eigen values and Eigen vectors by power method (3)

Interpolation- Newton’s divided difference, cubic spline, Hermite poly, error in

interpolation, Least square approximation. (6)

Numerical differentiation and integration (Trapezoidal rule, Simpson’s 1/3rd rule,

Simpson’s 3/8th rule), Error analysis. (5)

Numerical solution of ordinary differential equations (Taylor series method, Euler’s &

Modified Euler’s method, Runge-Kutta method), Finite difference solution of boundary

value problem. (9)

Numerical solution of partial differential equations of hyperbolic (wave equation),

parabolic (heat equation), elliptic (Laplace and Poisson equation) type. (9)

Text Books,

and/or

reference

books

Text Books:

1. Introductory Methods of Numerical Analysis- S.S.Sastry (PHI).

2. Numerical Methods for scientific & Engineering Computation- M.K. Jain, S.R.K.

Iyengar & R.K. Jain (New Age International (P) Ltd.).

Reference Books:

1. Numerical Mathematical Analysis- J.B. Scarborough (Oxford & IBH).

2. A friendly introduction to Numerical Analysis- Braine Bradie (Pearson Education).

Page 12 of 12


Course

Code


(PCR) /

Electives (PEL)


Lecture

(L)

Tutorial

(T)

Practical

(P)

Total

Hours

MAO843 Optimization

Techniques

PEL 3 0 0 3 3

Pre-requisites Vector Spaces and Matrices, Linear Transformations, Eigenvalues

and Eigenvectors Course

Outcomes CO1: Fundamentals of Linear Algebra CO2: Fundamentals of Differential Calculus CO3: Fundamentals of Vector Calculus CO4: Basic Concepts of Statistics

Topics

Covered

Basic Concepts: Formulation of mathematical programming problems; Classification of

optimization problems; Optimization techniques – classical and advanced techniques (5)

Optimization using Calculus: Convexity and concavity of functions of one and two

variables; Optimization of function of multiple variables subject to equality constraints;

Lagrangian function; Optimization of function of multiple variables subject to equality

constraints; Hessian matrix formulation (7)

Linear Programming: Standard form of linear programming (LP) problem; Canonical form

of LP problem; Assumptions in LP Models; Graphical method for two variable optimization

problem; Motivation of simplex method, Simplex algorithm and construction of simplex

tableau; Revised simplex method; Duality in LP; Primal dual relations; Dual Simplex

Method; Sensitivity or post optimality analysis; bounded variables; Examples for

transportation, assignment, TSP problems (18)

Dynamic Programming: Representation of multistage decision process; Types of

multistage decision problems; Concept of sub optimization and the principle of optimality

(8)

Integer Programming: Integer linear programming; Branch and Bound algorithm; Concept

of cutting plane method; Mixed integer programming; Solution algorithms (8)

Advanced Topics in Optimization: Direct and indirect search methods; Heuristic and Meta-

Heuristic Search methods; Multi objective optimization (10)

Text Books,

and/or

reference

material

Text Books: 1. Singiresu S. Rao, Engineering Optimization -Theory and Practice, New Age

International (P) Limited, New Delhi, 2000.

2. H.A. Taha, Operations Research: An Introduction, 5th Edition, Macmillan, New

York, 1992.

A. Ravindran, K. M. Ragsdell and G. V. Reklaitis, Engineering Optimization-

Methods and Applications, Wiley-India Edition, New Delhi, 2002.

Reference Books: 1. R. Fletcher, Optimization, Academic Press, 1969.

2. 2. K. Deb, Optimization for Engineering Design Algorithms and Examples, Prentice-

Hall of India Pvt. Ltd., New Delhi, 1995.

Sub Discipline: DEPARTMENTAL CORE

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